Replace the home hero with a spring carousel and default theme to light.

Adds Carousel under keep-alive-safe autoplay, peeks side cards past the container, and stops following the OS dark preference on first run.

Co-authored-by: Cursor <cursoragent@cursor.com>

docs/plans/2026-10-16-home-carousel-design.md

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+# Home Carousel — spring physics cards
+
+**Status:** approved  
+**Date:** 2026-10-16  
+**Scope:** `apps/user-app` home (`Carousel.vue` below `ShowcaseSlider`)
+
+## Intent
+
+A Framer-style spring carousel under the existing crossfade hero: center card large, side cards scaled down, infinite wrap, drag/flick with spring settle. Same admin slide images as `ShowcaseSlider`.
+
+## Decisions
+
+| Choice | Decision |
+|--------|----------|
+| Stack | Pure Vue SFC (no Swiper / Motion) |
+| Name / path | `components/home/Carousel.vue` |
+| Placement | Immediately below `ShowcaseSlider`, above `CategoryRail` |
+| Data | Same `slides` computed from admin home slider |
+| Props | `slides` (+ optional spring/layout knobs with defaults) |
+| Dots | Yes, pill style aligned with showcase |
+| Out of scope | Demo inspector panel, Prev/Next chrome, new admin API |
+
+## Motion defaults
+
+- `sideScale`: 0.60  
+- `gap`: 14px  
+- `borderRadius`: 22px (match ShowcaseSlider)  
+- Frame `aspect-ratio`: `320 / 208` (match ShowcaseSlider); center card full-bleed  
+
+- `stiffness`: 180  
+- `damping`: 22  
+- Internal layout `direction: ltr` (gesture still screen-space)  
+- Autoplay off by default; respect reduced-motion when enabled later  
+
+## Non-goals
+
+Replacing `ShowcaseSlider`, inventing slide destinations, or adding external animation libraries.